Moore Graph

In graph theory, a Moore graph is a regular graph of degree d and diameter k whose number of vertices equals the upper bound

An equivalent definition of a Moore graph is that it is a graph of diameter k with girth 2k + 1. Moore graphs were named by Hoffman & Singleton (1960) after Edward F. Moore, who posed the question of describing and classifying these graphs.

As well as having the maximum possible number of vertices for a given combination of degree and diameter, Moore graphs have the minimum possible number of vertices for a regular graph with given degree and girth. That is, any Moore graph is a cage (Erdõs, Rényi & Sós 1966). The formula for the number of vertices in a Moore graph can be generalized to allow a definition of Moore graphs with even girth as well as odd girth, and again these graphs are cages.

Read more about Moore Graph:  Bounding Vertices By Degree and Diameter, Moore Graphs As Cages, Examples

Famous quotes containing the words moore and/or graph:

    is an enchanted thing
    like the glaze on a
    katydid-wing
    —Marianne Moore (1887–1972)

    When producers want to know what the public wants, they graph it as curves. When they want to tell the public what to get, they say it in curves.
    Marshall McLuhan (1911–1980)